A short jump is just that. A jump that's shorter (or lower) than normal. Because they follow a quicker arc, they are often not punished with an anti-air except by the sharpest players. They are a great offensive tool that covers lots of ground, initiates offense from a jump move, creates long block-chains and is hard to punish. If you do not know how to deal with this especially in games like CvS2 where shortjumps are prominent, you will quickly find yourself guardbroken and dead.

In SF4, Zangief is the only character with a 'short jump'. You can perform this by tapping up, THEN a direction to shortjump in that direction. IE tap up, then upforward to shortjump forwards.